In Monday's other clash, US Open champion Coco Gauff opened her tournament with a 6-0, 6-1 drubbing of Tunisia's Ons Jabeur.
Polish star Swiatek looked out of sorts in an error-strewn first set in which she trailed 2-5 before roaring back to clinch a 7-6(3), 6-0 victory.
The 22-year-old four-time Grand Slam champion is bidding to reclaim her world number-one ranking from Aryna Sabalenka at this week's season-ending finals in Mexico.
However, that goal looked unlikely during a nervy opening from Swiatek, who was broken in her first service game before seventh seed Vondrousova held for a 2-0 lead.
Swiatek managed to claw the break back in the fourth game to square the first set at 2-2 but then fell to pieces as Vondrousova broke for a 3-2 lead and then held to go 4-2 up.
Another shaky service game from Swiatek ended in a break of serve to leave Vondrousova in the driving seat at 5-2.
But Vondrousova's game collapsed thereafter, and Swiatek broke back twice in quick succession to level the set at 5-5 before holding for 6-5.
Although Vondrousova steadied the ship to hold serve and set up a tie break, it was only a temporary reprieve.
Swiatek quickly took control of the breaker and clinched the set when Vondrousova double-faulted.
Vondrousova's service game went into meltdown in the second set, with Swiatek breaking her three times in a row.
Another Vondrousova double-fault left Swiatek 5-0 up, and the Pole sealed victory on her serve in the final game.
"In the first part of the match I wasn't feeling like I was playing bad," Swiatek said.
"I just felt like I was making mistakes on the last shots within the rally. I felt there was room for improvement but I didn't need to change a lot.
"So I just tried to be more precise, not play risky."
The 19-year-old Gauff raced through the first set against Jabeur to win 6-0 in just 23 minutes and then shrugged off a lengthy rain delay to take the second set 6-1 for a convincing win.
"Ons is a great player, so I felt really unsteady the whole match even though it didn't look like that," Gauff said.
"But I'm just happy to finally get a win here in this event."
The WTA Finals sees eight players divided into two groups of four playing in a round-robin first phase, with the top two in each group advancing to the semi-finals on Saturday.